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The lack of basic maths skills can be a major problem when it comes to nurses administering drugs to patients. Calculations are still a significant source of drug error.

Parenteral opiates are often relied on to manage acute pain in patients needing effective analgesia. But errors resulting in overdose of intravenous opiate can lead rapidly to respiratory depression. The opiate antagonist naloxone reverses opiate overdose and is usually needed quickly. However, this can cause confusion, because the product is prepared in micrograms. A small volume is involved, and the dose given needs to be titrated against response.

Postoperatively, the epidural route is now common for infusions of opiate and local anaesthetic. If opiates or, indeed, most drugs, have been calculated incorrectly, the consequences for patients can be serious.

If given in too high concentrations, local anaesthetic used in epidural infusions can cause extensive motor blockade, leading to immobility and pressure ulcers, which is distressing to the patient (Lee, 1991). Wheatley et al (2001) call for routine use of pre-filled epidural infusion bags to avoid the risk of calculation error when ward staff prepare infusions.

Nursing competence in drug calculations has been a cause for concern (Duffin, 2000; Coombes, 2000). Hutton (1998a) suggests that a degree of 'de-skilling' has resulted from the increasingly user-friendliness of drug preparations and widespread use of electronic drip counters.

Her research into students' competence in drug calculations demonstrated a marked improvement on initial test results after a structured revision programme.

Written accounts obtained from students in the study revealed that many felt unable to perform calculations such as long division and fractions without using a calculator, as they had come to rely on these at school.

There is some debate over calculator use. Hutton (1998b) argues that calculators are usually available in areas where calculations are complex, and that their use should be encouraged.

The opinion of the United Kingdom Central Council for Nursing, Midwifery and Health Visiting (UKCC) (now the Nursing and Midwifery Council) is that nurses should not rely too heavily on calculators.

The latest guidelines for the administration of medicines (UKCC, 2000) state that the use of calculators 'should not act as a substitute for arithmetical knowledge and skill'.

Developing calculation skills relies on understanding decimals to make conversion easier. And when using long division it is essential to get it the right way round. The use of simple, memorable formulae for regular reference can be a great help .

Drug calculationsDrug calculations appear to be impossibly difficult, unless you break them down into small steps. They are vitally important to get right, yet they are so easy to get wrong. This paper will now look at some commonly used drug calculations and the way that mistakes can happen.

Type A calculationsWhen the dose you want is not a whole ampoule.

For example:
- Prescription states 200mg (milligrams)
- You have an ampoule of 500mg (milligrams) in 4ml (millilitres).

What volume contains the dose you need?
If you have an ampoule of 500mg in 4ml, and you need 200mg, it can appear to be a daunting calculation. The first step is to find out what volume contains 1mg (4/500) and then multiply it by how many mg you want (200).

The easy way to remember this is the famous nursing equation:'What you want, over what you've got, times what it's in'

In this instance:200mg x 4ml / 500mg = 1.6ml

The common error here is to get it upside down, and divide what you've got by what you want. This fortunately gives you a stupid answer, which is obviously wrong, in this case 10ml. You already know that you need a fraction of an ampoule and not two and a bit ampoules, which highlights the error.

To help make sure you get it the right way up, remember WIG:What you Want x what it's In / What you've Got

Converting units
All weights, volumes and times in any equation must be in the same units. With weights the unit changes every thousand. For example, you need 1000 micrograms (mcg) to make 1 milligram (mg) and 1000 milligrams to make one gram (g) .

Type B calculations
These are infusion rate calculations.
For example:
- Prescription states 30 mg/hour
- You have a bag containing 250mg in 50ml

Therefore, at what rate (ml/hr) do you set the pump?

These are the same as type A calculations, only once you have worked out the volume that contains the amount of drug you need, you set the pump to give that amount per hour.

In this instance, work out how many ml contain ONE mg of drugUsing the WIG equation
30 x 50 / 250 = 6ml

Therefore the calculation shows that, to give 30mg per hour, the infusion pump rate would need to be set at 6ml per hour.

This calculation is straightforward when the rate you want (30mg/hour) and the amount of the drug in the bag (250mg) are both in the same units (mg).

However, if the infusion required that 600 micrograms were to be infused each hour instead, this would first need to be converted into mg before the infusion rate was calculated, that is, 600 micrograms = 0.6mg.

The equation for infusion rate calculation is dose stated in prescription (milligrams per hour) times volume in syringe (in millilitres) divided by the amount in the syringe (in milligrams) equals the infusion rate (millilitres per hour), or: